On the lift-optimal aspect ratio of a revolving wing at low Reynolds number

Abstract

Lentink & Dickinson (2009 , 2705-2719. (doi:10.1242/jeb.022269)) showed that rotational acceleration stabilized the leading-edge vortex on revolving, low aspect ratio (AR) wings and hypothesized that a Rossby number of around 3, which is achieved during each half-stroke for a variety of hovering insects, seeds and birds, represents a convergent high-lift solution across a range of scales in nature. Subsequent work has verified that, in particular, the Coriolis acceleration plays a key role in LEV stabilization. Implicit in these results is that there exists an optimal AR for wings revolving about their root, because it is otherwise unclear why, apart from possible morphological reasons, the convergent solution would not occur for an even lower Rossby number. We perform direct numerical simulations of the flow past revolving wings where we vary the AR and Rossby numbers independently by displacing the wing root from the axis of rotation. We show that the optimal lift coefficient represents a compromise between competing trends with competing time scales where the coefficient of lift increases monotonically with AR, holding Rossby number constant, but decreases monotonically with Rossby number, when holding AR constant. For wings revolving about their root, this favours wings of AR between 3 and 4.

Numerical predictions of low Reynolds number compressible aerodynamics

“…This phenomenon is also in line with previous numerical and experimental observations at low Reynolds numbers (e.g. [16,17,18]). is also very complex and cannot be captured through VLM.…”

A simple vortex-loop-based model for unsteady rotating wings

“…As mentioned above, it is assumed that the LEV stays attached along the -axis (or the wing) until the end of the motion. Jardin & Colonius (2018) showed that this is true approximately for a local Rossby number, , of , if the span is long enough to avoid nearby TV effects (see also Lentink & Dickinson 2009; Kruyt et al. 2015).…”

“…However, the LEV remains close to the wing over much of the span and the overall flow exhibits a growing vortex loop for up to , albeit with complex outboard structures (Garmann & Visbal 2014; Carr et al. 2015; Jardin & Colonius 2018). Therefore, the simplified assumptions of an attached LEV and large-scale, increasing loop structure are reasonable at least for the values tested in § 3.…”

Versatile reduced-order model of leading-edge vortices on rotary wings

“…However, when α is slightly less that 90 • , drops by a small amount. This effect can be attributed to the truncation error in (11). The vortex centroid position is the most sensitive to α when κ = 0; see Fig.…”

“…The growing amount of experimental and computational work during the past decade (e.g., Refs. [5][6][7][8][9][10][11]) opens new perspectives for reduced order modeling of the LEV of a rotating wing at large angle of attack. The latter approach has been so far less popular.…”